alleryThe function $f(x)=2x^3-6x^2+6x+5$ has critical point(s) at
A$x=0$ and $x=1$
B$x=2$ only
C$x=-1$ and $x=1$
D$x=1$ only
Answer & Solution
Correct answer: D. $x=1$ only
1. $f'(x)=6x^2-12x+6=6(x-1)^2$.
2. Set $f'(x)=0$: $(x-1)^2=0$.
3. The only solution is $x=1$ (a repeated root).
_Source: syllabus Mathematics Ch 6 "Application of Derivatives", p.19_
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